Transcript An Inverse Gibbs-Thomson Effect in Nanoporous Nanoparticles

An Inverse Gibbs-Thomson Effect in Nanoporous
Nanoparticles
Ian McCue
Jonah Erlebacher
Department of Materials
Science and Engineering
Materials Research Society,
November 29th, 2012
This work is supported by
NSF DMR 1003901
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Nanoporous Gold (NPG)
Characteristics of NPG
• bicontinuous, open porosity
• tunable pore size
~5 nm  10 microns via
electrochemical processing and/or
thermal annealing
• porosity is sub-grain size
NPG is not nanoparticulate
• porosity retains a long-range
single crystal network
grain boundary
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single-crystalline to a scale > 3
orders of magnitude larger than
any pore/ligament diameter
Electrochemistry of Porosity Evolution
The “critical potential” separates two potential windows:
• below Ec  planar, passivated morphologies
• sufficiently far above Ec  porosity evolution
What changes with potential?
• rate of silver dissolution (fast), surface diffusivity (slow)
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Formation Mechanism in Bulk Systems
A.
Nucleation and growth
of vacancy islands
B.
Development of
gold-passivated mounds
C.
Evolution of gold-poor
mound bases
D.
Mound undercutting,
nucleation of new gold
mounds, and pore
bifurcation
E.
Evolution of
gold-passivated porosity
F.
Post-dealloying
coarsening,
and/or further dissolution
Erlebacher, J., J. Electrochem. Soc. 151 (2004), C614
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Kinetic Monte Carlo (KMC):
A simulation tool to study coarsening
KMC Algorithm
simulated nanoporous metal
1. Tabulate all possible transitions ki 
real nanoporous gold
2. The time for an event to occurNwith
100% probability is: t   ln   ki
i 1
where  is a random number
in  0,1
3. Pick an event i to occur during theN
time interval with probability Pi  ki  k j 1
j 1
4. Move atoms corresponding to event i
5. Update neighbors, transition list, go
to step 2 and repeat
Rate Parameter for Surface Diffusion:
Rate Parameter for Dissolution:
 nE 
kdiff  v1 exp   B  v1  1013 sec1 EB  0.15eV n  coordination
 k bT 
 nEB    v  104 sec1   applied potential
kdiss  v2 exp  
kbT



2
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Nanoporous Nanoparticles
J. Snyder, J. Erlebacher
Initial Conditions
Looked at four different particle sizes: radii of 10, 15, 25 and 40 atoms
Looked at three different compositions: 65%, 75%, and 85% Ag
Simulations ran for 104-105 simulated seconds, or ~ 5 x108 iterations
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Gibbs-Thomson Effects on Electrochemical
Stability
•
•
•
•
L. Tang, B. Han, K. Persson, C. Friesen, T. He, K. Sieradzki, G.
Ceder, J. Electrochem.
Soc. 132, 596 (2010).
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Particle of radius r will
have additional surface
energy  increase per
atom by:
  2 r
where  is the atomic
vol.
Smaller means more
unstable
G-T effect manifests in
electrochemical stability
of nanoparticles
Decrease in dissolution
potential of atom by:
E   n
where n is the number of
electrons given up to
form metal cation
What about Binary Particles?
NO!
The potential we are
measuring is not a certain
critical current, but an
intrinsic potential based on
the propensity that a
particle will dealloy
•
•
Does not mean Ag atoms require more
energy to dissolve
As size decreases more potential is
required to form porosity
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Porosity Evolution in Nanoparticles
•
Low-coordination
surface silver sites
are dissolved
•
Surface gold
atoms quickly
passivate the
surface
•
Regions of bulk
are exposed due
to fluctuations in
the outermost
layer and porosity
can occur
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Porosity Evolution in Nanoparticles (cont)
Below Ep
Smaller volume
corresponds to
fully dealloyed
particles
Diffuse
threshold
between
passivation
and porosity
evolution
1:1 Ratio
Above Ep
Larger volume
corresponds to
passivated
particles
Define Ep as potential where the distribution area of each Gaussian was equal
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Observation on Porosity Evolution in NP
Surface
Diffusion events
are controlled
by kink
fluctuations
Ag terrace
atoms are the
rate limiting step
in dissolution
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Kinetic Derivation
Can setup a first order rate equation for the
change in the number of surface silver atoms
dNAg
 kdiss Pkink Pperc NAg
dt
kdiss   exp    9 EB  EP  k BT 
Probability of Au fluctuation at a kink site
Probability Ag atom is connected to bulk Ag atoms
Equilibrium Number of Ag atoms on the surface
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Solution to Kinetic Equation
•
•
Single dissolution event at the passivated state leads to
porosity evolution
Simplest criterion for Ep is that over a time interval ∆t- the
lifetime of the step edge fluctuation- is that N Ag  t   N Ag  0  1
 
 

N

0

1
1

EP  9EB  kbT ln 
ln  Ag
 
vP
P

t
N
0

perc
Ag
 kink

 
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Percolation Probability for Surface Ag Atoms
What does percolation probability mean:
• Can we trace a path of silver atoms from one side of the
particle to the other
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Number of Ag Terrace Atoms
As particle size
increases:
• Facet size
does not
appreciably
increase
• Ag atoms are
found on the
edges of
facets
• As a result the
number of Ag
terrace sites
scales with the
radius
Ag terrace atoms
distributed evenly
across facets
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Surface Diffusion
Radius 10
Radius 40
Key points:
• Peak at ~10-6 corresponds to adatom fluctuations
• Peak at ~101 corresponds to fluctuations at step edges
• Area under kink interval curve corresponds to Pkink
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Evaluation of Kinetic Expression
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Summary
• Porosity evolution in nanoparticles is dependent on a chorus
of size dependent variables and exhibits rich complexity
• Gibbs-Thomson effects dictate the size dependence, but not
as we initially expected
• First order rate equation gives an awesome fit to our observed
results
• Major conclusion is that surface diffusion changes the critical
potential
• Could potentially tailor porosity in nanoparticles adding an
alloying component that will kill the formation of a
passivating monolayer
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Acknowledgements
• Jonah Erlebacher
• Erlebacher Research Group
• Josh Snyder
• Ellen Benn
• Felicitee Kertis
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